Registration of 3-D intraoperative MR images of the brain using a finite-element biomechanical model

We present a new algorithm for the nonrigid registration of three-dimensional magnetic resonance (MR) intraoperative image sequences showing brain shift. The algorithm tracks key surfaces of objects (cortical surface and the lateral ventricles) in the image sequence using a deformable surface matching algorithm. The volumetric deformation field of the objects is then inferred from the displacements at the boundary surfaces using a linear elastic biomechanical finite-element model. Two experiments on synthetic image sequences are presented, as well as an initial experiment on intraoperative MR images showing brain shift. The results of the registration algorithm show a good correlation of the internal brain structures after deformation, and a good capability of measuring surface as well as subsurface shift. We measured distances between landmarks in the deformed initial image and the corresponding landmarks in the target scan. Cortical surface shifts of up to 10 mm and subsurface shifts of up to 6 mm were recovered with an accuracy of 1 mm or less and 3 mm or less respectively.     

Displacement estimation with co-registered ultrasound for image guided neurosurgery: a quantitative in vivo porcine study

Brain shift during open cranial surgery presents a challenge for maintaining registration with image-guidance systems. Ultrasound (US) is a convenient intraoperative imaging modality that may be a useful tool in detecting tissue shift and updating preoperative images based on intraoperative measurements of brain deformation. We have quantitatively evaluated the ability of spatially tracked freehand US to detect displacement of implanted markers in a series of three in vivo porcine experiments, where both US and computed tomography (CT) image acquisitions were obtained before and after deforming the brain. Marker displacements ranged from 0.5 to 8.5 mm. Comparisons between CT and US measurements showed a mean target localization error of 1.5 mm, and a mean vector error for displacement of 1.1 mm. Mean error in the magnitude of displacement was 0.6 mm. For one of the animals studied, the US data was used in conjunction with a biomechanical model to nonrigidly re-register a baseline CT to the deformed brain. The mean error between the actual and deformed CT's was found to be on average 1.2 and 1.9 mm at the marker locations depending on the extent of the deformation induced. These findings indicate the potential accuracy in coregistered freehand US displacement tracking in brain tissue and suggest that the resulting information can be used to drive a modeling re-registration strategy to comparable levels of agreement.     

In vivo quantification of retraction deformation modeling for updated image-guidance during neurosurgery

The use of coregistered preoperative anatomical scans to provide navigational information in the operating room has greatly benefited the field of neurosurgery. Nonetheless, it has been widely acknowledged that significant errors between the operating field and the preoperative images are generated as surgery progresses. Quantification of tissue shift can be accomplished with volumetric intraoperative imaging; however, more functional, lower cost alternative solutions to this challenge are desirable. We are developing the strategy of exploiting a computational model driven by sparse data obtained from intraoperative ultrasound and cortical surface tracking to warp preoperative images to reflect the current state of the operating field. This paper presents an initial quantification of the predictive capability of the current model to computationally capture tissue deformation during retraction in the porcine brain. Performance validation is achieved through comparisons of displacement and pressure predictions to experimental measurements obtained from computed tomographic images and pressure sensor recordings. Group results are based upon a generalized set of boundary conditions for four subjects that, on average, account for at least 75% of tissue motion generated during interhemispheric retraction. Individualized boundary conditions can improve the degree of data-model match by 10% or more but warrant further study. Overall, the level of quantitative agreement achieved in these experiments is encouraging for updating preoperative images to reflect tissue deformation resulting from retraction, especially since model improvements are likely as a result of the intraoperative constraints that can be applied through sparse data collection.     

In vivo quantification of a homogeneous brain deformation model for updating preoperative images during surgery

Clinicians using image-guidance for neurosurgical procedures have recently recognized that intraoperative deformation from surgical loading can compromise the accuracy of patient registration in the operating room. While whole brain intraoperative imaging is conceptually appealing it presents significant practical limitations. Alternatively, a promising approach may be to combine incomplete intraoperatively acquired data with a computational model of brain deformation to update high resolution preoperative images during surgery. The success of such an approach is critically dependent on identifying a valid model of brain deformation physics. Towards this end, we evaluate a three-dimensional finite element consolidation theory model for predicting brain deformation in vivo through a series of controlled repeat-experiments. This database is used to construct an interstitial pressure boundary condition calibration curve which is prospectively tested in a fourth validation experiment. The computational model is found to recover 75%-85% of brain motion occurring under loads comparable to clinical conditions. Additionally, the updating of preoperative images using the model calculations is presented and demonstrates that model-updated image-guided neurosurgery may be a viable option for addressing registration errors related to intraoperative tissue motion.     

Stereopsis-guided brain shift compensation

Brain deformation models have proven to be a powerful tool in compensating for soft tissue deformation during image-guided neurosurgery. The accuracy of these models can be improved by incorporating intraoperative measurements of brain motion. We have designed and implemented a passive intraoperative stereo vision system capable of estimating the three-dimensional shape of the surgical scene in near real-time. This intraoperative shape is compared with the cortical surface in the co-registered preoperative magnetic resonance (MR) volume for the estimation of the cortical motion resulting from the open cranial surgery. The estimated cortical motion is then used to guide a full brain model, which updates a preoperative MR volume. We have found that the stereo vision system is accurate to within approximately 1 mm. Based on data from two representative clinical cases, we show that stereopsis guidance improves the accuracy of brain shift compensation both at and below the cortical surface.     

Image-Guided Intraoperative Cortical Deformation Recovery Using Game Theory: Application to Neocortical Epilepsy Surgery

During neurosurgery, nonrigid brain deformation prevents preoperatively-acquired images from accurately depicting the intraoperative brain. Stereo vision systems can be used to track intraoperative cortical surface deformation and update preoperative brain images in conjunction with a biomechanical model. However, these stereo systems are often plagued with calibration error, which can corrupt the deformation estimation. In order to decouple the effects of camera calibration from the surface deformation estimation, a framework that can solve for disparate and often competing variables is needed. Game theory, which was developed to handle decision making in this type of competitive environment, has been applied to various fields from economics to biology. In this paper, game theory is applied to cortical surface tracking during neocortical epilepsy surgery and used to infer information about the physical processes of brain surface deformation and image acquisition. The method is successfully applied to eight in vivo cases, resulting in an 81% decrease in mean surface displacement error. This includes a case in which some of the initial camera calibration parameters had errors of 70%. Additionally, the advantages of using a game theoretic approach in neocortical epilepsy surgery are clearly demonstrated in its robustness to initial conditions.      

Model-updated image guidance: initial clinical experiences with gravity-induced brain deformation

Image-guided neurosurgery relies on accurate registration of the patient, the preoperative image series, and the surgical instruments in the same coordinate space. Recent clinical reports have documented the magnitude of gravity-induced brain deformation in the operating room and suggest these levels of tissue motion may compromise the integrity of such systems. We are investigating a model-based strategy which exploits the wealth of readily-available preoperative information in conjunction with intraoperatively acquired data to construct and drive a three dimensional (3-D) computational model which estimates volumetric displacements in order to update the neuronavigational image set. Using model calculations, the preoperative image database can be deformed to generate a more accurate representation of the surgical focus during an operation. In this paper, we present a preliminary study of four patients that experienced substantial brain deformation from gravity and correlate cortical shift measurements with model predictions. Additionally, we illustrate our image deforming algorithm and demonstrate that preoperative image resolution is maintained. Results over the four cases show that the brain shifted, on average, 5.7 mm in the direction of gravity and that model predictions could reduce this misregistration error to an average of 1.2 mm.     

A computational model for tracking subsurface tissue deformationduring stereotactic neurosurgery

Recent advances in the field of sterotactic neurosurgery have made it possible to coregister preoperative computed tomography (CT) and magnetic resonance (MR) images with instrument locations in the operating field. However, accounting for intraoperative movement of brain tissue remains a challenging problem. While intraoperative CT and MR scanners record concurrent tissue motion, there is motivation to develop methodologies which would be significantly lower in cost and more widely available. The approach the authors present is a computational model of brain tissue deformation that could be used in conjunction with a limited amount of concurrently obtained operative data to estimate subsurface tissue motion. Specifically, the authors report on the initial development of a finite element model of brain tissue adapted from consolidation theory. Validations of the computational mathematics in two and three dimensions are shown with errors of 1%-2% for the discretizations used. Experience with the computational strategy for estimating surgically induced brain tissue motion in vivo is also presented. While the predicted tissue displacements differ from measured values by about 15%, they suggest that exploiting a physics-based computational framework for updating preoperative imaging databases during the course of surgery has considerable merit. However, additional model and computational developments are needed before this approach can become a clinical reality     

Estimating Brain Deformation During Surgery Using Finite Element Method: Optimization and Comparison of Two Linear Models

This paper addresses estimation of brain deformation during craniotomy using finite element modeling. Two mechanical models are optimized and compared for this purpose: linear solid-mechanic model and linear elastic model. Both models assume the realistic finite deformation of the brain after opening the skull. In this study, we use pre-operative and intra-operative magnetic resonance images (MRI) of five patients undergoing brain tumor surgery. Anatomical landmarks are identified by an expert radiologist on MRI and used for the method development and comparison studies. We use tetrahedral finite element meshes and optimize model parameters by minimizing the mean distance between the predicted locations of the anatomical landmarks using the pre-operative images and their actual locations on the intra-operative images. Evaluation of the objective function using a second set of landmarks not used in the optimization process suggests that accuracy of the solid mechanic model is higher than that of the elastic model for our application. Visual inspection of the results confirms this conclusion. The proposed method along with the location information of the surface landmarks measured in the operating room and marked on the pre-operative images can be used to estimate the brain deformations without needing intra-operative images. In this case, since the parameters of the brain tissue are not the same for different patients, the proposed optimization process is crucial for obtaining accurate results.     

Biomechanical modeling of the human head for physically based, nonrigid image registration

The accuracy of image-guided neurosurgery generally suffers from brain deformations due to intraoperative changes. These deformations cause significant changes of the anatomical geometry (organ shape and spatial interorgan relations), thus making intraoperative navigation based on preoperative images error prone. In order to improve the navigation accuracy, we developed a biomechanical model of the human head based on the finite element method, which can be employed for the correction of preoperative images to cope with the deformations occurring during surgical interventions. At the current stage of development, the two-dimensional (2-D) implementation of the model comprises two different materials, though the theory holds for the three-dimensional (3-D) case and is capable of dealing with an arbitrary number of different materials. For the correction of a preoperative image, a set of homologous landmarks must be specified which determine correspondences. These correspondences can be easily integrated into the model and are maintained throughout the computation of the deformation of the preoperative image. The necessary material parameter values have been determined through a comprehensive literature study. Our approach has been tested for the case of synthetic images and yields physically plausible deformation results. Additionally, we carried out registration experiments with a preoperative MR image of the human head and a corresponding postoperative image simulating an intraoperative image. We found that our approach yields good prediction results, even in the case when correspondences are given in a relatively small area of the image only.     

Intraoperative brain shift compensation: accounting for dural septa

Biomechanical models that describe soft tissue deformation provide a relatively inexpensive way to correct registration errors in image-guided neurosurgical systems caused by nonrigid brain shift. Quantifying the factors that cause this deformation to sufficient precision is a challenging task. To circumvent this difficulty, atlas-based methods have been developed recently that allow for uncertainty, yet still capture the first-order effects associated with deformation. The inverse solution is driven by sparse intraoperative surface measurements, which could bias the reconstruction and affect the subsurface accuracy of the model prediction. Studies using intraoperative MR have shown that the deformation in the midline, tentorium, and contralateral hemisphere is relatively small. The dural septa act as rigid membranes supporting the brain parenchyma and compartmentalizing the brain. Accounting for these structures in models may be an important key to improving subsurface shift accuracy. A novel method to segment the tentorium cerebelli will be described, along with the procedure for modeling the dural septa. Results in seven clinical cases show a qualitative improvement in subsurface shift accuracy making the predicted deformation more congruous with previous observations in the literature. The results also suggest a considerably more important role for hyperosmotic drug modeling for the intraoperative shift correction environment.     

Robust nonrigid registration to capture brain shift from intraoperative MRI

We present a new algorithm to register 3-D preoperative magnetic resonance (MR) images to intraoperative MR images of the brain which have undergone brain shift. This algorithm relies on a robust estimation of the deformation from a sparse noisy set of measured displacements. We propose a new framework to compute the displacement field in an iterative process, allowing the solution to gradually move from an approximation formulation (minimizing the sum of a regularization term and a data error term) to an interpolation formulation (least square minimization of the data error term). An outlier rejection step is introduced in this gradual registration process using a weighted least trimmed squares approach, aiming at improving the robustness of the algorithm. We use a patient-specific model discretized with the finite element method in order to ensure a realistic mechanical behavior of the brain tissue. To meet the clinical time constraint, we parallelized the slowest step of the algorithm so that we can perform a full 3-D image registration in 35 s (including the image update time) on a heterogeneous cluster of 15 personal computers. The algorithm has been tested on six cases of brain tumor resection, presenting a brain shift of up to 14 mm. The results show a good ability to recover large displacements, and a limited decrease of accuracy near the tumor resection cavity.     

Compensating for intraoperative soft-tissue deformations using incomplete surface data and finite elements

Image-guided liver surgery requires the ability to identify and compensate for soft tissue deformation in the organ. The predeformed state is represented as a complete three-dimensional surface of the organ, while the intraoperative data is a range scan point cloud acquired from the exposed liver surface. The first step is to rigidly align the coordinate systems of the intraoperative and preoperative data. Most traditional rigid registration methods minimize an error metric over the entire data set. In this paper, a new deformation-identifying rigid registration (DIRR) is reported that identifies and aligns minimally deformed regions of the data using a modified closest point distance cost function. Once a rigid alignment has been established, deformation is accounted for using a linearly elastic finite element model (FEM) and implemented using an incremental framework to resolve geometric nonlinearities. Boundary conditions for the incremental formulation are generated from intraoperatively acquired range scan surfaces of the exposed liver surface. A series of phantom experiments is presented to assess the fidelity of the DIRR and the combined DIRR/FEM approaches separately. The DIRR approach identified deforming regions in 90% of cases under conditions of realistic surgical exposure. With respect to the DIRR/FEM algorithm, subsurface target errors were correctly located to within 4 mm in phantom experiments.     

Measurement and analysis of brain deformation during neurosurgery

Recent studies have shown that the surface of the brain is deformed by up to 20 mm after the skull is opened during neurosurgery, which could lead to substantial error in commercial image-guided surgery systems. We quantitatively analyze the intraoperative brain deformation of 24 subjects to investigate whether simple rules can describe or predict the deformation. Interventional magnetic resonance images acquired at the start and end of the procedure are registered nonrigidly to obtain deformation values throughout the brain. Deformation patterns are investigated quantitatively with respect to the location and magnitude of deformation, and to the distribution and principal direction of the displacements. We also measure the volume change of the lateral ventricles by manual segmentation. Our study indicates that brain shift occurs predominantly in the hemisphere ipsi-lateral to the craniotomy, and that there is more brain deformation during resection procedures than during biopsy or functional procedures. However, the brain deformation patterns are extremely complex in this group of subjects. This paper quantitatively demonstrates that brain deformation occurs not only at the surface, but also in deeper brain structure, and that the principal direction of displacement does not always correspond with the direction of gravity. Therefore, simple computational algorithms that utilize limited intraoperative information (e.g., brain surface shift) will not always accurately predict brain deformation at the lesion.     

Phenomenological model of diffuse global and regional atrophy using finite-element methods

The main goal of this work is the generation of ground-truth data for the validation of atrophy measurement techniques, commonly used in the study of neurodegenerative diseases such as dementia. Several techniques have been used to measure atrophy in cross-sectional and longitudinal studies, but it is extremely difficult to compare their performance since they have been applied to different patient populations. Furthermore, assessment of performance based on phantom measurements or simple scaled images overestimates these techniques' ability to capture the complexity of neurodegeneration of the human brain. We propose a method for atrophy simulation in structural magnetic resonance (MR) images based on finite-element methods. The method produces cohorts of brain images with known change that is physically and clinically plausible, providing data for objective evaluation of atrophy measurement techniques. Atrophy is simulated in different tissue compartments or in different neuroanatomical structures with a phenomenological model. This model of diffuse global and regional atrophy is based on volumetric measurements such as the brain or the hippocampus, from patients with known disease and guided by clinical knowledge of the relative pathological involvement of regions and tissues. The consequent biomechanical readjustment of structures is modelled using conventional physics-based techniques based on biomechanical tissue properties and simulating plausible tissue deformations with finite-element methods. A thermoelastic model of tissue deformation is employed, controlling the rate of progression of atrophy by means of a set of thermal coefficients, each one corresponding to a different type of tissue. Tissue characterization is performed by means of the meshing of a labelled brain atlas, creating a reference volumetric mesh that will be introduced to a finite-element solver to create the simulated deformations. Preliminary work on the simulation of acquisition artefacts is also presented. Cross-sectional and longitudinal sets of simulated data are shown and a visual classification protocol has been used by experts to rate real and simulated scans according to their degree of atrophy. Results confirm the potential of the proposed methodology.     

Brain shift estimation in image-guided neurosurgery using 3-D ultrasound

Intraoperative brain deformation is one of the most important causes affecting the overall accuracy of image-guided neurosurgical procedures. One option for correcting for this deformation is to acquire three-dimensional (3-D) ultrasound data during the operation and use this data to update the information provided by the preoperatively acquired MR data. For 12 patients 3-D ultrasound images have been reconstructed from freehand sweeps acquired during neurosurgical procedures. Ultrasound data acquired prior to and after opening the dura, but prior to surgery, have been quantitatively compared to the preoperatively acquired MR data to estimate the rigid component of brain shift at the first stages of surgery. Prior to opening the dura the average brain shift measured was 3.0 mm parallel to the direction of gravity, with a maximum of 7.5 mm, and 3.9 mm perpendicular to the direction of gravity, with a maximum of 8.2 mm. After opening the dura the shift increased on average 0.2 mm parallel to the direction of gravity and 1.4 mm perpendicular to the direction of gravity. Brain shift can be detected by acquiring 3-D ultrasound data during image-guided neurosurgery. Therefore, it can be used as a basis for correcting image data and preoperative planning for intraoperative deformations.     

Validation of finite element models of liver tissue using micro-CT

In this work, we aim at validating some soft tissue deformation models using high-resolution micro-computed tomography (Micro-CT) images. The imaging technique plays a key role in detecting the tissue deformation details in the contact region between the tissue and the surgical tool (probe) for small force loads and provides good capabilities of creating accurate 3-D models of soft tissues. Surgical simulations rely on accurate representation of the mechanical response of soft tissues subjected to surgical manipulations. Several finite-element models have been suggested to characterize soft tissues. However, validating these models for specific tissues still remain a challenge. In this study, ex vivo lamb liver tissue is chosen to validate the linear elastic model (LEM), the linear viscoelastic model (LVEM), and the neo-Hooke hyperelastic model (NHM). We find that the LEM is more applicable to lamb liver than the LVEM for smaller force loads (< 20 g) and that the NHM is closer to reality than the LVEM for the range of force loads from 5 to 40 g.     

Simulation of tissue atrophy using a topology preserving transformation model

We propose a method to simulate atrophy and other similar volumetric change effects on medical images. Given a desired level of atrophy, we find a dense warping deformation that produces the corresponding levels of volumetric loss on the labeled tissue using an energy minimization strategy. Simulated results on a real brain image indicate that the method generates realistic images of tissue loss. The method does not make assumptions regarding the mechanics of tissue deformation, and provides a framework where a pre-specified pattern of atrophy can readily be simulated. Furthermore, it provides exact correspondences between images prior and posterior to the atrophy that can be used to evaluate provisional image registration and atrophy quantification algorithms.     

Modeling of Soft Poroelastic Tissue in Time-Harmonic MR Elastography

Elastography is an emerging imaging technique that focuses on assessing the resistance to deformation of soft biological tissues in vivo. Magnetic resonance elastography (MRE) uses measured displacement fields resulting from low-amplitude, low-frequency (10 Hz-1 kHz) time-harmonic vibration to recover images of the elastic property distribution of tissues including breast, liver, muscle, prostate, and brain. While many soft tissues display complex time-dependent behavior not described by linear elasticity, the models most commonly employed in MRE parameter reconstructions are based on elastic assumptions. Further, elasticity models fail to include the interstitial fluid phase present in vivo. Alternative continuum models, such as consolidation theory, are able to represent tissue and other materials comprising two distinct phases, generally consisting of a porous elastic solid and penetrating fluid. MRE reconstructions of simulated elastic and poroelastic phantoms were performed to investigate the limitations of current-elasticity-based methods in producing accurate elastic parameter estimates in poroelastic media. The results indicate that linearly elastic reconstructions of fluid-saturated porous media at amplitudes and frequencies relevant to steady-state MRE can yield misleading effective property distributions resulting from the complex interaction between their solid and fluid phases.     

Volume registration using needle paths and point landmarks for evaluation of interventional MRI treatments

We created a method for three-dimensional (3-D) registration of medical images (e.g., magnetic resonance imaging (MRI) or computed tomography) to images of physical tissue sections or to other medical images and evaluated its accuracy. Our method proved valuable for evaluation of animal model experiments on interventional-MRI guided thermal ablation and on a new localized drug delivery system. The method computes an optimum set of rigid body registration parameters by minimization of the Euclidean distances between automatically chosen correspondence points, along manually selected fiducial needle paths, and optional point landmarks, using the iterative closest point algorithm. For numerically simulated experiments, using two needle paths over a range of needle orientations, mean voxel displacement errors depended mostly on needle localization error when the angle between needles was at least 20 degrees. For parameters typical of our in vivo experiments, the mean voxel displacement error was < 0.35 mm. In addition, we determined that the distance objective function was a useful diagnostic for predicting registration quality. To evaluate the registration quality of physical specimens, we computed the misregistration for a needle not considered during the optimization procedure. We registered an ex vivo sheep brain MR volume with another MR volume and tissue section photographs, using various combinations of needle and point landmarks. Mean registration error was always < or = 0.54 mm for MR-to-MR registrations and < or = 0.52 mm for MR to tissue section registrations. We also applied the method to correlate MR volumes of radio-frequency induced thermal ablation lesions with actual tissue destruction. In this case, in vivo rabbit thigh volumes were registered to photographs of ex vivo tissue sections using two needle paths. Mean registration errors were between 0.7 and 1.36 mm over all rabbits, the largest error less than two MR voxel widths. We conclude that our method provides sufficient spatial correspondence to facilitate comparison of 3-D image data with data from gross pathology tissue sections and histology.